Introduction

Background information

The International Monitoring System (IMS) element of the verification regime of the Comprehensive Nuclear-Test-Ban Treaty (CTBT) uses four technologies to monitor the globe for indications of nuclear explosions, which are absolutely prohibited by the treaty. Infrasound, seismic, and hydroacoustic monitoring technologies are used to detect indications of nuclear explosions in the Earth’s atmosphere, underground, and underwater, respectively. A fourth monitoring technology is used to detect radioactive particulates and noble gases indicative of nuclear explosions. Of these monitoring technologies, the radionuclide monitoring technology is particularly important in that it is the only technology that is capable of providing conclusive evidence that a suspected nuclear explosion was in-fact a nuclear explosion as opposed to a large conventional explosion [1].

In the event the IMS element of the verification regime of the CTBT should register a detection characteristic of a nuclear explosion, the On-Site Inspection (OSI) element of the CTBT could allow a team of inspectors to go to the suspected nuclear explosion site to gather data and facts so that the member states to the CTBT may assess the details of the event. The same radionuclide monitoring technologies utilized by the IMS element of the verification regime of the CTBT would be used during an OSI [1].

In practice, the process of detecting radioactive noble gases and then demonstrating conclusively that they originated from a nuclear explosion is complicated by the presence of radioactive noble gases produced by non-explosion sources. The same radioxenons that are of interest in nuclear explosion monitoring—131mXe, 133mXe, 133Xe, and 135Xe—are also released by radiopharmaceutical facilities, commercial nuclear power plants, and nuclear research reactors. The radioxenon background activity concentrations resulting from these types of facilities have been studied quite extensively [2–10]. Natural processes such as spontaneous fission and cosmic-ray induced reactions also contribute to radioxenon and radioargon background activity concentrations. While natural sources of radioactive noble gases have received less attention to-date than the aforementioned man-made sources, several studies have been conducted [11–16]. These studies are the subject of the next section.

Radioactive noble gas background activity concentration studies conducted to-date

Some of the earliest radioactive noble gas background activity concentration studies were conducted by Hebel [11, 12]. Hebel identified the various processes by which the radioxenon isomers and isotopes of most interest in nuclear explosion monitoring (131mXe, 133mXe, 133Xe, and 135Xe) are produced in nature and then calculated the activity concentrations resulting from some of the more important processes, including spontaneous fission of 238U and cosmic-neutron-induced fission of 232Th, 235U, and 238U, across a number geologiesFootnote 1. Hebel’s theoretical radioxenon background activity concentration calculations were an extension of the work of Fabryka-Martin [17] and relied on a postulated cosmic neutron flux profile and geological composition data, reaction cross-section data, and fission yield data taken from the literature [11, 12]. The 133Xe background activity concentration estimates generated by Hebel at a depth of 1 m in granite and limestone are presented in Table 1 alongside shallow subsurface 133Xe and 37Ar background activity concentrations associated with a sampling of other geologies. It should be noted that Hebel’s activity concentrations account for the emanation of radioxenon out of the rock matrix and into the geological pore volumes, but diffusion of the radioxenons out of the geological pore volumes to the atmosphere is not accounted for [11, 12].

Table 1 Summary of select radioactive noble gas background activity concentrations taken from the literature
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Additional radioactive noble gas background activity concentration studies were conducted by Riedmann and Purtschert [13]. While Hebel focused on studying the radioxenon activity concentrations resulting from various natural processes, Riedmann and Purtschert focused on the 37Ar activity concentrations resulting from cosmic-neutron-induced activation of 40Ca. In their work, Riedmann and Purtschert developed theoretical 37Ar activity concentration profiles for a number of sampling locations and geologies. They also measured the 37Ar activity concentrations at several of the same locations and geologies and found that their measurements were in close agreement with their theoretical activity concentration profiles [13]. The measured 37Ar activity concentrations reported by Riedmann and Purtschert for a geology high in Ca are presented in Table 1.

More recently, Lowrey [14] studied the radioxenon background activity concentrations resulting from spontaneous fission and cosmic-neutron-induced reactions and also the radioargon background activity concentrations resulting from cosmic-neutron- and cosmic-μ-induced reactions as part of a larger study investigating the subsurface transport of radioactive noble gases. As was the case with the studies conducted by Hebel and Riedmann and Purtschert, Lowrey’s radioactive noble gas background activity concentration calculations relied on geological composition data, cosmic neutron flux profiles, reaction cross-section data, fission yield data, and radioactive decay constants taken from the literature [14]. The 133Xe and 37Ar background activity concentrations reported by Lowrey at a depth of 1 m in a high-Ca granite as well as a sandstone are presented in Table 1.

The most detailed radioactive noble gas background concentration studies conducted to-date were carried out by Johnson et al. [15, 16]. Johnson et al. used an MCNP6 model to generate cosmic neutron flux profiles specific to several different points in the solar cycle, several different locations, and several different geologies. The remainder of the inputs to the calculations of Johnson et al. were taken from the literature [15, 16]. The 133Xe and 37Ar background activity concentrations reported by Johnson et al. at a depth of 1 m in carbonate rock and limestone are presented in Table 1.

Limitations of studies conducted to-date and need for additional studies

A review of the radioactive noble gas background activity concentrations reproduced in Table 1 reveals that the 133Xe and 37Ar background activity concentrations resulting from natural processes in different locations and geologies may span several orders of magnitude. Furthermore, given that the detection limits associated with the CTBT 133Xe and 37Ar field detection systems [18–20] are about 2.0 and 20 mBq m−3, respectively [21], in some cases the radioxenon and radioargon activity concentrations resulting from natural processes may be high enough to be detected during a CTBT OSI. Table 1 also reveals that while the various studies conducted to-date have produced results that are in good general agreement with one another, in some cases there are order-of-magnitude differences between predictions, even within a given geology.

In this paper we describe the development of an MCNP6 model and a suite of supporting MATLAB scripts that will ultimately be used to conduct detailed studies of the variables most important in establishing the radioactive noble gas background activity concentrations resulting from cosmic-neutron-induced reactions in the Earth’s atmosphere, in various geologies, and in seawater. The objective of these studies is to further develop our understanding of the variables that are most important in establishing the radioactive noble gas background activity concentrations not only across a sampling of geologies, but also within a given geology. The emphasis will be on the variables involved in the production of radioactive noble gases via cosmic-neutron-induced reactions. Radioactive noble gas background activity concentrations resulting from spontaneous fission will not be considered. The sensitivities to variables associated with gas emanation and transport processes will not be studied here either.

Theory and methodology

Production of radionuclides via neutron-induced reactions

In this section we derive some basic expressions to calculate the equilibrium activity concentrations of radionuclides produced via cosmic-neutron-induced fission and cosmic-neutron-induced activation reactions. We begin by recognizing that the rate at which the atom concentration of some radionuclide i, which is assumed to be produced only via cosmic-neutron-induced fission and to be lost only via radioactive decay, changes with time may be calculated according to Eq. (1):

$$ \frac{{{\text{d}}N_{i} \left( t \right)}}{{{\text{d}}t}} = \mathop \int \nolimits_{0}^{\infty } \varPhi \left( {E,t} \right) \cdot N_{T} \cdot \sigma_{f,T} \left( E \right) \cdot \chi_{i,T} \left( E \right) \cdot dE - \lambda_{i} \cdot N_{i} \left( t \right) $$
(1)

In Eq. (1), N i (t) is the time-dependent atom concentration of radionuclide i, Φ(E, t) is the energy- and time-dependent cosmic neutron flux, N T is the atom concentration of target atom T, σ f,T (E) is the energy-dependent fission cross-section of target atom T, χ i,T (E) is the energy-dependent yield of radionuclide i from fissions of target atom T, and λ i is the radioactive decay constant associated with radionuclide i. If we assume that the system has reached equilibrium (a relatively good assumption given that the solar cycle has an 11 year period and the cosmic neutron flux varies relatively slowly with time) we can drop the time dependence from Eq. (1) and set the differential term equal to zero. Doing this and also recognizing that the \( \lambda_{i} \cdot N_{i} \left( t \right) \) term on the right side of the equal sign in Eq. (1) is the radionuclide activity concentration we wish to solve for allows us to write the following expression for the equilibrium activity concentration of radionuclide i, A i , where again, production from cosmic-neutron-induced fission is assumed to be equal to loses to radioactive decay:

$$ A_{i} = \mathop \int \nolimits_{0}^{\infty } \varPhi \left( E \right) \cdot N_{T} \cdot \sigma_{f,T} \left( E \right) \cdot \chi_{i,T} \left( E \right) \cdot dE $$
(2)

Now, to compute the radionuclide activity concentration resulting from fissions induced by incident cosmic neutrons of all energies we must either (a) evaluate the integral on the right hand side of Eq. (2), or (b) create a set of discrete energy-dependent terms in Eq. (2) and calculate the total radionuclide activity concentration as a summation over all energy groups. Here we will take the later approach, and the expression for the equilibrium activity concentration of radionuclide i, which again, is assumed to be produced only via cosmic-neutron-induced fission and lost only via radioactive decay, becomes the following:

$$ A_{i} = \mathop \sum \limits_{E = 1}^{{n_{E} }} \varPhi_{E} \cdot N_{T} \cdot \sigma_{f,T,E} \cdot \chi_{i,T,E} $$
(3)

The derivation of the equilibrium activity concentration of some radionuclide i, which is assumed to be produced only via cosmic-neutron-induced activation and to be lost only via radioactive decay, is very similar to the derivation given above. The initial expression describing the rate at which the atom concentration of the radionuclide changes with time is given by Eq. (4):

$$ \frac{{dN_{i} \left( t \right)}}{dt} = \mathop \int \nolimits_{0}^{\infty } \varPhi \left( {E,t} \right) \cdot N_{T} \cdot \sigma_{a,T} \left( E \right) \cdot dE - \lambda_{i} \cdot N_{i} \left( t \right) $$
(4)

Applying the same simplifying assumptions we applied above and creating a set of discrete energy-dependent terms in Eq. (4) allows us to write the following expression for the equilibrium activity concentration of radionuclide i, which again, is assumed to be produced only via neutron-induced activation and lost only via radioactive decay:

$$ A_{i} = \mathop \sum \limits_{E = 1}^{{n_{E} }} \varPhi_{E} \cdot N_{T} \cdot \sigma_{a,T,E} $$
(5)

In the sections that follow we describe the development of the inputs required to evaluate Eqs. (3) and (5).

The MCNP6 model and the suite of supporting MATLAB scripts

One of the novel aspects of the radioactive noble gas background activity concentration studies documented here is we use a high-resolution MCNP6 model to generate cosmic neutron flux profiles specific to each of the scenarios studied. The MCNP6 model allows us to generate cosmic neutron flux profiles, and thus radioargon and radioxenon background activity concentration estimates, that are specific to various dates, locations (latitudes/longitudes), atmospheric conditions, geologies, and seawater conditions. In this section we describe some of the aspects of the MCNP6 model that are hard-coded into the model. We also introduce the suite of supporting MATLAB scripts developed to automate the process of incorporating the scenario-specific high-resolution data into the MCNP6 model.

A schematic representation of our MCNP6 model is presented in Fig. 1. Conceptually, this model is very similar to the MCNP6 model used by Johnson et al. [15, 16]. The model uses the cosmic-ray source term built into version 1 of MCNP6 [22] to simulate a cosmic-ray flux incident upon the Earth’s atmosphere at an altitude of 65 km. The cosmic-ray source term is new to version 1 of MCNP6 and currently consists of α-particles (~10 %) and protons (~90 %) [22]. MCNP6 transports these source particles down through the atmospheric layers of the model, creating the secondary particles of interest (cosmic neutrons) via various spallation reactions in the upper layers of the atmosphere. The cosmic neutrons are then transported down through the atmospheric layers of the model and into the subsurface.

Fig. 1
figure 1

Schematic representation of the MCNP6 model

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Like the model used by Johnson et al., the model described here dictates the use of the ENDF/B-VII.1 nuclear data libraries [23, 24] and the CEM03.03 intra-nuclear cascade physics model [22, 25, 26] coupled with the LAQGSM high-energy physics model (the Los Alamos Quark–Gluon String Model) [22, 26]. The model also specifies the use of reduced model transition energies on the MCNP6 LCB card [22, 27]. These settings are all in accordance with the recommendations of McKinney et al. [27]. The outer model geometry—an infinite cylinder with a specularly reflecting inner surface and an outer radius of 1 km—is also unchanged relative to the model used by Johnson et al. [15, 16].

The biggest difference between the MCNP6 model described here and the MCNP6 model used by Johnson et al. is the resolution of the atmospheric, geological, and seawater data incorporated into the model. The incorporation of high-resolution scenario-specific data was made possible by the development of a suite of supporting MATLAB scripts that automate the task of processing the scenario-specific data and then incorporating the data into the MCNP6 model. The MATLAB script suite currently consists of six sets of MATLAB scripts, or modules. An overview of the modules, their interconnections, and the tasks performed by each module is presented in Fig. 2.

Fig. 2
figure 2

Processing and flow of data and information within the suite of supporting MATLAB scripts

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The first module of the MATLAB script suite reads a formatted input file that contains all of the scenario-specific information needed to build the MCNP6 model. The formatted input file consists of a general information section, an atmospheric information section, and some number of geological information sections and/or seawater information sections, as applicable to a given scenario. The general information section of the formatted input file contains the general information specific to a given scenario, such as the date and location information associated with the scenario; this information is needed to define the date- and location-specific cosmic-ray source term in the MCNP6 model and is passed directly to the sixth module of the MATLAB script suite, which will be described shortly. The atmospheric, geological, and seawater information is passed to modules two, three, and four of the MATLAB script suite, respectively, for processing.

The second module of the MATLAB script suite generates (1) an atom concentration profile, (2) molecular, elemental, and isotopic composition information, and (3) a temperature profile for the atmospheric layers of the MCNP6 model according to the instructions provided by the user in the atmospheric information section of the formatted input file. The user can instruct the module to generate the aforementioned pieces of atmospheric information in one of two ways. The first option is to manually define the pressure and temperature profiles associated with the atmospheric layers of the MCNP6 model and then allow the module to generate an atom concentration profile and molecular, elemental, and isotopic composition information using the ideal gas law and atmospheric composition information taken from the U.S. Standard Atmosphere, 1976 [28]. The second option is to specify the use of a reference model, two of which are currently supported: the first is the U.S. Standard Atmosphere, 1976 [28], and the second is the standard atmosphere as defined by international standard ISO 2533 [29]. When using the second option the user simply specifies an atmospheric segmentation scheme and the module develops an atom concentration profile, molecular, elemental, and isotopic composition information, and a temperature profile applicable to the segmentation scheme in accordance with the rules of the referenced atmospheric model. In the formatted input file the user can also request that compositional variations be introduced into the atmospheric layers of the MCNP6 model. This is useful when conducting sensitivity studies in that the user must only specify the desired variations relative to the base atmospheric composition and the composition of the atmosphere is renormalized automatically by the module. Atmospheric composition variations may be incorporated into the MCNP6 model regardless of the option used to develop the base atmospheric composition.

The third module of the MATLAB script suite generates (1) an atom concentration profile and (2) molecular, elemental, and isotopic composition information for the geological layers of the MCNP6 model according to the instructions provided by the user in the geological information section of the formatted input file. The base composition for the geological layers of the model is read from a separate input file, directions to which must be provided by the user in the formatted input file. The atom concentrations associated with the geological layers of the MCNP6 model are calculated from the geological composition information and a user-specified geological mass density. The temperature profile associated with the geological layers of the MCNP6 model must be fully defined by the user in the formatted input file. As with the atmospheric layers, the user may request that compositional variations be incorporated into the geological layers of the MCNP6 model in the formatted input file.

The fourth module of the MATLAB script suite generates (1) an atom concentration profile, (2) molecular, elemental, and isotopic composition information, and (3) a temperature profile for the seawater layers of the MCNP6 model according to the instructions provided by the user in the seawater information section of the formatted input file. The user can instruct the seawater module to generate this information in one of two ways. The first option is to manually define a segmentation scheme and the pressure, salinity, and temperature profiles associated with the seawater layers of the MCNP6 model and then allow the seawater module to use the international equation of state of seawater [30–33] to generate an atom concentration profile for the seawater layers of the MCNP6 model. The second option is to provide the seawater pressure, salinity, and temperature profiles in the form of a separate input file having the native World Ocean Database (WOD) [34] format. The seawater module is capable of parsing individual pressure, salinity, and temperature datasets from the WOD-formatted file and eliminating bad datasets from consideration based on the values assigned to quality control and user flags built into the WOD datasets. The WOD datasets that remain after the quality control checks are then passed to the international equation of state of seawater [30–33] and used to generate an atom concentration profile for the seawater layers. As with the atmospheric and geological layers of the MCNP6 model, the user can request that compositional variations be introduced into the seawater layers of the MCNP6 model in the formatted input file.

The fifth module of the MATLAB script suite is a support module. It generates isotopic composition vectors for each of the atmospheric, geological, and seawater layers of the MCNP6 model from the molecular, elemental, and isotopic composition information generated by the atmospheric, geological, and seawater modules. The isotopic composition vectors are passed to the sixth module of the MATLAB script suite, which also receives as inputs the segmentation schemes, atom concentration profiles, and temperature profiles generated by the atmospheric, geological, and seawater modules and writes all the information to an MCNP6 input deck. The MCNP6 input deck is written in a form such that it is completely ready to submit for execution.

As illustrated by Fig. 2, two additional MATLAB script suite modules are still under development. Module 7, will be a second support module. It will accept the isotopic composition vectors generated by Module 5 as inputs and then query several nuclear data libraries (ENDF/B-VII.1 [23, 24], JEFF 3.2 [35], JENDL 4.0u2 [36], etc.) and extract nuclear data for each of the isotopes associated with the isotopic composition vectors as it is available. Module 8, will be used to generate NJOY 2012 [37] input decks to support Doppler broadening the nuclear data gathered by Module 7 to the temperatures associated with each of the atmospheric, geological, and seawater layers of the MCNP6 model. This Doppler broadened nuclear data will also be run through the ACER module of NJOY 2012, which re-writes the nuclear data in a file format that may be read by MCNP6, and then stored in a directory where all the scenario-specific nuclear data may be accessed by MCNP6. But again, Modules 7 and 8 are still under development; the results documented here were generated using only the ENDF/B-VII.1 nuclear data libraries packaged with version 1 of MCNP6.

Inputs supporting initial scoping and validation studies

We used the MCNP6 model and the suite of supporting MATLAB scripts described in the preceding section to generate 37Ar, 131mXe, 133mXe, 133Xe, and 135Xe background activity concentration estimates for two layers of the Earth’s atmosphere, a depth of 1 m in a geology representative of the Earth’s upper crust, and a depth of 5 m in seawater. The date associated with all of these estimates was 10 June 2005, which is the most recent date on which the sunspot number associated with our sun was at the mean value taken over the period 1 January 1960 through 31 December 2005 (the range of dates for which actual cosmic-ray flux data is available in version 1 of MCNP6 [22]). Selecting a date with a sunspot number that is representative of the mean sunspot number results in the introduction of a cosmic-ray source term representative of the mean cosmic-ray flux profile into the MCNP6 model. The cosmic-ray source term was placed at a geometric height of 65 km in the atmosphere, which is the default in version 1 of MCNP6. The location was set to 45°0′0″N, 65°0′0″E. The latitude was set to 45°0′0″N for consistency with the U.S. Standard Atmosphere, 1976 [28], which was developed specifically for this latitude. Setting the latitude to 45°0′0″N is also beneficial in that the intensity of the cosmic ray flux is at its mean value at this latitude [15, 16].

To develop the atmospheric layers of our MCNP6 model we used the U.S. Standard Atmosphere, 1976 [28] atmospheric model built into the atmospheric module of the MATLAB script suite. For the atmospheric segmentation scheme we requested 1 m segments extending from 0.5 m above the Earth’s surface up to a geometric height of 9.5 m. This segmentation scheme supported tallying the neutron flux at 1 m intervals centered at 1, 2, 3 m, etc. up to 9 m, and should be sufficient to support evaluating the radioargon and radioxenon background activity concentrations associated with the first few meters of the Earth’s atmosphere. We then requested 100 m segments from 9.5 m up to the cosmic-ray source term at 65 km. The only exception to this was a 1 m segment centered at 15 km that supported another neutron flux tally. The atmospheric atom concentration and temperature profiles generated by the atmospheric module of the MATLAB script suite are presented in Fig. 3.

Fig. 3
figure 3

Atmospheric atom concentration and temperature profiles

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For the geological layers of the MCNP6 model we used a base elemental composition representative of the Earth’s upper crust [38]. This elemental composition consists largely of Si (303,480 ppm), Al (77,440 ppm), Fe (30,890 ppm), Ca (29,450 ppm), Na (25,670 ppm), Mg (13,510 ppm), and K (28,650 ppm). The Th and U concentrations were set to 10.3 and 2.5 ppm, respectively [38]. We assumed a geological density of 2.6 g cm−3 [39], and a uniform temperature profile equal to 288.15 K. The geological segmentation scheme was set such that the subsurface was divided into 1 m segments extending from 0.5 m below the Earth’s surface down to a depth of 25.5 m. This segmentation scheme supported tallying the neutron flux in 1 m intervals centered at 1, 2, 3 m, etc. down through 25 m, and should be sufficient to support evaluating the radioargon and radioxenon background activity concentrations associated with the depths at which soil gas activity concentration measurements might be made during a CTBT OSI.

For the seawater estimates we used the seawater module of the MATLAB script suite to process a set of seawater pressure, salinity, and temperature datasets downloaded from the WOD [34]. The seawater datasets were returned by a WOD query that requested all the Conductivity-Temperature-Depth (CTD) datasets associated with the 2 month period centered about 10 June 2005 and a latitude of 45°0′0″N. The query returned 381 CTD datasets, 295 of which passed all the quality control and user flag checks. The seawater module used the international equation of state of seawater [30–33] to calculate the seawater mass density associated with each of the seawater pressure, salinity, and temperature triplets. The seawater data was then binned according to a segmentation scheme in which the seawater layers were broken into 5 m segments centered at depths of 5, 10, 15 m, etc. down through 50 m. We would have liked the seawater segmentation scheme to be a bit finer, but the WOD CTD datasets contain a relatively small number of data points very near the seawater surface and so we had to make the segmentation scheme relatively course to get good average values for the seawater layers near the surface. However, we are currently working on a change to the seawater module of the MATLAB script suite that should allow us to use finer seawater segmentation schemes going forward.

After binning the data, the seawater module calculated the mean mass density, the mean salinity, and the mean temperature associated with each of the seawater layers. It used these mean values to identify the single WOD dataset that was most representative of all the WOD datasets returned by the WOD dataset query. The density, salinity, and temperature profiles associated with the selected WOD dataset are presented in Fig. 4. Figure 4 also shows the profiles associated with the other WOD datasets returned by the WOD dataset query and the mean mass density, the mean salinity, and the mean temperature associated with each of the seawater layers.

Fig. 4
figure 4

Seawater density, salinity, and temperature profiles

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The seawater module then evaluated the seawater salt constituent atom concentrations for each of the seawater layers by evaluating the product of the seawater layer mass density, the seawater layer salinity, and the mass fraction associated with each of the seawater salt constituents. The seawater salt mass fractions were taken from Castro and Huber [40]. The seawater Th and U atom concentrations were set to 1.6 × 10−7 and 3.3 × 10−3 ppm, respectively [41, 42]. The remainder of the seawater was assumed to be H2O.

Results

A selection of the cosmic neutron flux profiles generated by our MCNP6 model using the atmospheric, geological, and seawater inputs described in the previous section are presented in Fig. 5. The cosmic neutron flux profile at a depth of 1 m in the Earth’s upper crust is in good agreement with the cosmic neutron flux profiles generated by Johnson et al. [15, 16]. The trends in the cosmic neutron flux profiles also look reasonable. The neutron flux profile becomes more thermalized as it passes down through the Earth’s atmosphere and into the subsurface, with the degree of thermalization being more pronounced in the seawater scenarios than it is in the scenarios employing a geology representative of the Earth’s upper crust. Furthermore, the magnitude of the neutron flux is seen to decrease at increasing depths in both the Earth’s upper crust and in seawater.

Fig. 5
figure 5

Neutron flux profiles

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We used the neutron flux profiles presented in Fig. 5 as inputs to Eqs. (3) and (5) and calculated the radioxenon and radioargon background activity concentrations resulting from cosmic-neutron-induced reactions at a geometric height of 15 km in the Earth’s atmosphere, at a geometric height of 1 m above a geology representative of the Earth’s upper crust, at a geometric height of 1 m above seawater, at a depth of 1 m in a geology representative of the Earth’s upper crust, and a depth of 5 m in seawater. The 40Ca, 232Th, 235U, and 238U target atom concentrations used as inputs to Eqs. (3) and (5) were consistent with the concentrations used as inputs to our MCNP6 model. For the reaction cross-section inputs we used the group weighted ENDF/B-VII.1 reaction cross-sections generated by our MCNP6 model, and for the 232Th, 235U, and 238U fission yields we used the ENDF/B-VII.1 values [23, 24]. The results of our calculations are presented in Tables 2 and 3.

Table 2 Equilibrium radioargon background activity concentrations
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Table 3 Equilibrium radioxenon background activity concentrations
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The upper crust background activity concentrations reported in Tables 2 and 3 are in good general agreement with the values from the literature reproduced in Table 1. The 37Ar background activity concentrations at 1 m over both the Earth’s upper crust and seawater are less than 1 mBq m−3 and appear to be in good agreement with the atmospheric 37Ar background activity concentration expected by Haas et al. [21]. The 37Ar background activity concentration at a depth of 1 m in the Earth’s upper crust is roughly three orders of magnitude larger than the 37Ar background activity concentration at a depth of 5 m in seawater. This seems reasonable given that the product of the neutron flux and the 40Ca target atom concentration in the Earth’s upper crust is roughly three orders of magnitude larger than the product of the neutron flux and the 40Ca target atom concentration in seawater. And finally, the radioxenon background activity concentrations at a depth of 1 m in the Earth’s upper crust are all roughly six orders of magnitude larger than the radioxenon background activity concentrations at a depth of 5 m in seawater. Again, these differences seem reasonable given that the product of the neutron flux and the sum of the 232Th, 235U, and 238U target atom concentrations in the Earth’s upper crust is roughly six orders of magnitude larger than the product of the neutron flux and the sum of the 232Th, 235U, and 238U target atom concentrations in seawater.

Conclusions and future work

In this paper we describe the development of an MCNP6 model and a suite of supporting MATLAB scripts that will ultimately be used to conduct detailed studies of the radioactive noble gas background activity concentrations resulting from cosmic-neutron-induced reactions in the Earth’s atmosphere, in various geologies, and in seawater. To this point, the model has been used to generate cosmic neutron flux profiles for two layers of the Earth’s atmosphere, a geology representative of the Earth’s upper crust, and seawater. These neutron flux profiles were used to calculate the radioargon and radioxenon background activity concentrations resulting from a variety of cosmic-neutron-induced reactions. The radioargon and radioxenon background activity concentrations were found to be in good general agreement with the background activity concentrations reported in the literature.

The MCNP model and suite of supporting MATLAB scripts described in this paper will ultimately be used to perform a series of detailed sensitivity studies. The objective of these studies is to develop our understanding of the variables that are most important in establishing the radioactive noble gas background activity concentrations in the Earth’s atmosphere, in various geologies, and in seawater. While the suite of supporting MATLAB scripts is still under development, the fact that the results documented herein are in good agreement with the results taken from the literature is encouraging.